Golf ball dimple surface

ABSTRACT

Golf ball dimples having a surface defined by a mode, or a weighted superposition of multiple modes, of oscillation of an n-sided polygon shaped membrane are disclosed.

FIELD OF THE INVENTION

The present invention relates to a golf ball dimple having a shape defined by a mode, or a weighted superposition of multiple modes, of oscillation of an n-sided polygon shaped membrane.

BACKGROUND OF THE INVENTION

Golf ball dimples are known to have a significant effect on the aerodynamic forces acting on the ball during flight. For example, the dimples on a golf ball create a turbulent boundary layer around the ball. The turbulence energizes the boundary layer and helps it stay attached further around the ball to reduce the area of the wake. This greatly increases the pressure behind the ball and substantially reduces the drag. Based on the significant role that dimples play in golf ball design, manufacturers continually seek to develop novel dimple patterns, sizes, shapes, volumes, cross-sections, etc. Thus, the present invention provides a novel dimple design having unique aesthetic and aerodynamic characteristics.

SUMMARY OF THE INVENTION

In one embodiment, the present invention is directed to a golf ball having a plurality of recessed dimples on the surface thereof, wherein at least a portion of the recessed dimples have a surface defined by a mode, or a weighted superposition of multiple modes, of oscillation of an n-sided polygon shaped membrane. The membrane extends over a domain which fits inside a circumscribed circle having a diameter of from 0.005 inches to 0.350 inches.

BRIEF DESCRIPTION OF DRAWINGS

In the accompanying drawings, which form a part of the specification and are to be read in conjunction therewith, and which are given by way of illustration only, and thus are not meant to limit the present invention:

FIG. 1 shows a dimple cross-sectional profile according to an embodiment of the present invention;

FIG. 2 is a perspective view of the dimple in FIG. 1;

FIG. 3 shows a dimple cross-sectional profile according to an embodiment of the present invention; and

FIG. 4 is a perspective view of the dimple in FIG. 3.

DETAILED DESCRIPTION

Conventional golf ball dimples have a cross-sectional profile defined by a 2-dimensional curve that is rotated about a vertical axis to create the dimple surface. The present invention discloses a new method for designing a golf ball dimple by modeling the dimple as a mode, or a weighted superposition of multiple modes, of oscillation of an n-sided polygon shaped membrane.

While the present invention is discussed below with respect to a four-sided polygon shaped membrane, it is understood that the present invention is not limited to such, and that any n-sided polygon shaped membrane can be used.

Considering a four-sided polygon shaped membrane, the membrane extends over a domain, D, defined by 0<x<d_(x) and 0<y<d_(y), where d_(x) and d_(y) are dimple dimensions, and which fits inside a circumscribed circle having a diameter d_(d), wherein d_(d) is from 0.005 inches to 0.350 inches, or d_(d) is 0.005 inches or 0.020 inches or 0.100 inches or 0.220 inches or 0.250 inches or 0.350 inches, or d_(d) is within a range having a lower limit and an upper limit selected from these values.

Assuming the mass density of the membrane is constant, the differential equation to describe the membrane's motion is:

$\begin{matrix} {{{{{\bigtriangledown^{2}{W\left( {x,y} \right)}} + {\beta^{2}{W\left( {x,y} \right)}}} = 0},{{{where}\mspace{14mu} \beta^{2}} = \frac{{\rho\omega}^{2}}{T}}}{{{and}\mspace{14mu} \bigtriangledown^{2}} = {\frac{\partial^{2}}{\partial x} + {\frac{\partial^{2}}{\partial y^{2}}.}}}} & \left\lbrack {{Equation}\mspace{14mu} 1} \right\rbrack \end{matrix}$

The equation is solved as a membrane fixed at all boundaries, and assuming the following boundary conditions:

-   -   W(0, y)=0, W(a, y)=0     -   W(x, 0)=0, W(x, b)=0

Utilizing the method of separation of variables, a solution to Equation 1 will have the form of:

W(x,y)=X(x)Y(y)  [Equation 2],

leading to:

$\begin{matrix} {{\frac{\partial^{2}{X(x)}}{\partial x^{2}} + {\alpha^{2}{X(x)}}} = {0\mspace{14mu} {and}}} & \left\lbrack {{Equation}\mspace{14mu} 3} \right\rbrack \\ {{{\frac{\partial^{2}{Y(y)}}{\partial y^{2}} + {\gamma^{2}{Y(y)}}} = 0}\mspace{11mu}} & \left\lbrack {{Equation}\mspace{14mu} 4} \right\rbrack \end{matrix}$

where α²⁺γ²=β².

Thus, the solution of Equation 3 is:

X(x)=C ₁ sin(αx)+C ₂ cos(αx)  [Equation 5]

and the solution of Equation 4 is:

Y(y)=C ₃ sin(γy)+C ₄ cos(γy)  [Equation 6]

Substituting Equations 5 and 6 into Equation 2 yields:

W(x,y)=C ₁ sin(αx)+C ₂ cos(αx)+C ₃ sin(γy)+C ₄ cos(γy)  [Equation 7]

Assuming the above stated boundary conditions, the modes of oscillation can be written as:

$\begin{matrix} {{W\left( {x,y} \right)}_{mn} = {A_{mn}{\sin \left( \frac{m\; \pi \; x}{a} \right)}{\sin \left( \frac{n\; \pi \; y}{b} \right)}}} & \left\lbrack {{Equation}\mspace{14mu} 8} \right\rbrack \end{matrix}$

which can be manipulated for dimple design to be:

$\begin{matrix} {{W\left( {x,y} \right)}_{mn} = {C_{d}{\sin \left( \frac{m\; \pi \; x}{a} \right)}{\sin \left( \frac{n\; \pi \; y}{b} \right)}}} & \left\lbrack {{Equation}\mspace{14mu} 9} \right\rbrack \end{matrix}$

where C_(d) is the chord depth (in inches), and m and n are constants.

FIGS. 1 and 2 show a dimple cross-sectional profile and a perspective view, respectively, of a dimple according to an embodiment of the present invention wherein m is −1, n is 1, and C_(d) is 0.01 inches.

FIGS. 3 and 4 show a dimple cross-sectional profile and a perspective view, respectively, of a dimple according to an embodiment of the present invention wherein m is −2, n is 3, and C_(d) is 0.01 inches.

For purposes of the present invention, chord depth is defined as the maximum height or depth of the dimple with respect to the hob surface, whichever value is greater. Chord depth must be defined in this fashion due to the multitude of inflection points a given dimple designed using this method may have. The chord depth of dimples having a shape defined according to the present invention is typically 0.001 inches or 0.005 inches or 0.007 inches or 0.010 inches or 0.015 inches or 0.030 inches, or is within a range having a lower limit and an upper limit selected from these values.

The edge angle of dimples having a shape defined according to the present invention is typically 1° or 5° or 90° or 100°, or is within a range having a lower limit and an upper limit selected from these values.

The volume ratio, V₀, for dimples having a shape defined according to the present invention is the fractional ratio of the dimple volume, V_(d), divided by the volume of a like n-sided polygon, V_(p), with identical dimensions and depth equal to the chord depth, C_(d), of the dimple. The volume ratio is typically 0.001 or 0.05 or 0.96 or 1.0 or is within a range having a lower limit and an upper limit selected from these values.

Dimples having a shape defined according to the present invention may be described as concave up or concave down.

Dimples having a shape defined according to the present invention may have any number of inflection points.

In a particular embodiment, the present invention is directed to dimples having a surface defined by a single mode of oscillation of an n-sided polygon shaped membrane. In another particular embodiment, the present invention is directed to dimples having a surface defined by the weighted superposition of a combination of two or more modes of oscillation of an n-sided polygon shaped membrane. Dimples defined by the weighted superposition of two or more shapes are further disclosed, for example, in U.S. Patent Application Publication No. 2013/0172125, the entire disclosure of which is hereby incorporated herein by reference.

The present invention is not limited by any particular dimple pattern. Examples of suitable dimple patterns include, but are not limited to, phyllotaxis-based patterns; polyhedron-based patterns; and patterns based on multiple copies of one or more irregular domain(s) as disclosed in U.S. Pat. No. 8,029,388, the entire disclosure of which is hereby incorporated herein by reference; and particularly dimple patterns suitable for packing dimples on seamless golf balls. Non-limiting examples of suitable dimple patterns are further disclosed in U.S. Pat. Nos. 7,927,234, 7,887,439, 7,503,856, 7,258,632, 7,179,178, 6,969,327, 6,702,696, 6,699,143, 6,533,684, 6,338,684, 5,842,937, 5,562,552, 5,575,477, 5,957,787, 5,249,804, 5,060,953, 4,960,283, and 4,925,193, and U.S. Patent Application Publication Nos. 2006/0025245, 2011/0021292, 2011/0165968, and 2011/0183778, the entire disclosures of which are hereby incorporated herein by reference. Non-limiting examples of seamless golf balls and methods of producing such are further disclosed, for example, in U.S. Pat. Nos. 6,849,007 and 7,422,529, the entire disclosures of which are hereby incorporated herein by reference.

In a particular embodiment, the dimple pattern provides for overall dimple coverage of 60% or greater, or 65% or greater, or 75% or greater, or 80% or greater, or 85% or greater, or 90% or greater.

Golf balls of the present invention typically have a dimple count within a limit having a lower limit of 250 and an upper limit of 350 or 400 or 450 or 500. In a particular embodiment, the dimple count is 252 or 272 or 302 or 312 or 320 or 328 or 332 or 336 or 340 or 352 or 360 or 362 or 364 or 372 or 376 or 384 or 390 or 392 or 432.

Preferably, at least 30%, or at least 50%, or at least 60%, or at least 80%, or at least 90%, or at least 95% of the total number of dimples have a shape defined by a mode, or a weighted superposition of multiple modes, of oscillation of an n-sided polygon shaped membrane, with the remaining dimples, if any, having a plan shape and a cross-sectional profile based on any known dimple plan and profile shape Among the dimples having a shape defined according to the present invention, the shape of one dimple may be the same as or different from the shape of another dimple. Similarly, among the remaining dimples, if any, having a known dimple plan shape and profile shape, the plan shape and/or profile shape of one dimple may be the same as or different from the plan shape and/or profile shape of another dimple.

The present invention is not limited by any particular golf ball construction or any particular composition for forming the golf ball layers. For example, dimples having a shape according to the present invention can be used to form dimples on one-piece, two-piece (i.e., a core and a cover), multi-layer (i.e., a core of one or more layers and a cover of one or more layers), and wound golf balls, having a variety of core structures, intermediate layers, covers, and coatings.

When numerical lower limits and numerical upper limits are set forth herein, it is contemplated that any combination of these values may be used.

All patents, publications, test procedures, and other references cited herein, including priority documents, are fully incorporated by reference to the extent such disclosure is not inconsistent with this invention and for all jurisdictions in which such incorporation is permitted.

While the illustrative embodiments of the invention have been described with particularity, it will be understood that various other modifications will be apparent to and can be readily made by those of ordinary skill in the art without departing from the spirit and scope of the invention. Accordingly, it is not intended that the scope of the claims appended hereto be limited to the examples and descriptions set forth herein, but rather that the claims be construed as encompassing all of the features of patentable novelty which reside in the present invention, including all features which would be treated as equivalents thereof by those of ordinary skill in the art to which the invention pertains. 

What is claimed is:
 1. A golf ball having a plurality of recessed dimples on the surface thereof, wherein at least a portion of the recessed dimples have a surface defined by a mode of oscillation of a n-sided polygon shaped membrane, wherein the membrane extends over a domain which fits inside a circumscribed circle having a diameter of from 0.005 inches to 0.350 inches.
 2. The golf ball of claim 1, wherein the n-sided polygon is a four-sided polygon.
 3. The golf ball of claim 1, wherein the n-sided polygon is an irregular polygon.
 4. The golf ball of claim 1, wherein the polygon is a regular polygon selected from the group consisting of triangles, squares, rectangles, pentagons, hexagons, heptagons, and octagons.
 5. The golf ball of claim 1, wherein the domain fits inside a circumscribed circle having a diameter of from 0.020 inches to 0.250 inches.
 6. The golf ball of claim 1, wherein the domain fits inside a circumscribed circle having a diameter of form 0.100 inches to 0.220 inches.
 7. The golf ball of claim 1, wherein the dimples having a surface defined by a mode of oscillation of a n-sided polygon shaped membrane have a chord depth of from 0.001 inches to 0.030 inches.
 8. The golf ball of claim 1, wherein the dimples having a surface defined by a mode of oscillation of a n-sided polygon shaped membrane have a chord depth of from 0.005 inches to 0.015 inches.
 9. The golf ball of claim 1, wherein the dimples having a surface defined by a mode of oscillation of a n-sided polygon shaped membrane have a chord depth of from 0.007 inches to 0.010 inches.
 10. The golf ball of claim 1, wherein the dimples having a surface defined by a mode of oscillation of a n-sided polygon shaped membrane have an edge angle of from 1° to 100°.
 11. The golf ball of claim 1, wherein the dimples having a surface defined by a mode of oscillation of a n-sided polygon shaped membrane have an edge angle of from 5° to 90°. 